دانلود رایگان مقاله اصلاح فرمولاسیون جریمه ضعیف نوسانات کشش در عناصر رابط

Abstract

A frequently used approach to modeling of fracture along predefined paths (e.g. grain boundaries in metals) is to use intrinsic interface elements. Despite their popularity, it is well known that the use of such elements in combination with a stiff cohesive zone model may result in traction oscillations. A common strategy to alleviate this problem is to employ reduced Lobatto integration along the cohesive surface. Even though such reduced integration has been demonstrated to work well for some cases, the present work shows that there are situations where the use of this integration method results in severe traction oscillations. More precisely, it is shown that intrinsic interface elements (with full or reduced integration) share stability properties with an equivalent mixed formulation, and hence oscillations result from the violation of the inf–sup (LBB) condition for the mixed formulation. As a remedy for these oscillations, the interface elements are modified using a weak penalty formulation, based on a traction approximation fulfilling the inf–sup condition. Using this method, oscillation free results can be obtained without modifying the cohesive zone law or introducing additional unknowns. These oscillation free results are demonstrated by several numerical examples, including straight, curved and intersecting cracks.

4. Conclusions

In this paper, spurious traction oscillations in intrinsic interface elements are discussed. It is shown that these oscillations are related to violation of the inf–sup (LBB) condition and a remedy using a weak penalty formulation is proposed. Based on the analysis of the inf–sup condition, the occurrence of traction oscillations for the standard displacement based formulation is discussed: in addition to the oscillations reported in previous research when applying full Gauss integration [1], it is shown that oscillations may also appear when using two-point Lobatto integration and one-point integration. This is an important observation, because these two methods have been previously proposed as remedies for traction oscillations [1,21]. While the results confirm the non-oscillating behavior of Lobatto integration for the straight crack studied in [1], it is shown that both this integration scheme and full Gauss integration may lead to severe oscillations for curved or intersecting cracks with anisotropic cohesive zone models. Furthermore, the results indicate that one-point integration may work well for some cases involving curved cracks, whereas severe oscillations can occur for straight or intersecting cracks. Thus, attempting to alleviate traction oscillations using the standard displacement based formulation with reduced integration is in general highly problematic.